Segregated Nuts

Researchers use computer simulations to gain insights to the self-segregation …

While the mechanics of how a fluid flows are relatively well understood through the Navier-Stokesequation and its solutions (often numerical) in various geometries, the flow of granular materials is not understood nearly as well. Granular materials — while rather simple (sands, powders) — exhibit extremely complex flow phenomena. While extensive experimental and theoretical work has gone into understanding granular flow, the dynamics exhibited are too complex to be described with a single equation, as is the case in fluids. One particular difference is that granular mixtures will often separate under flow conditions. This can be extremely problematic if you are looking to create a homogeneous mixture of various granular materials as if often the case in mining operations, metallurgy, and the pharmaceutical industry.

Recently event-driven computer simulations (ED) have been used to further the understanding of why even simple, idealized granular mixtures segregate under certain conditions (Physical Review Letters). The simulations were of a binary mixture undergoing vibration on a flat bed (Figure to the right). The mixture studied consisted of two types of hard disks, small "host" disks that represented the majority of the mixture, and larger "intruder" disks that were the subject of the study. This is easily visualized as a large box with lots and lots of golf balls and a softball or two thrown in as intruders. By shaking the bed the researchers were able to study the dynamics of the intruder particle(s), and put forth a theory as to why they may segregate.

When only one intruder (large) particle was present (the classic BrazilNutProblem) the simulation demonstrated that the intruder particle would rise or fall due to buoyancy effects, as if it was swimming in a sea of the smaller particles. If its density was similar to that of the sea of smaller particles, then it could freely swim about throughout the sea (measured by studying its relative position as a function of time). While interesting in its own right, the Brazil Nut Effect, while closely related, is not what they set out to examine. The heart of this work is in gaining understanding of what happens when multiple intruder particles are present in the system. If the multiple intruders behave in a manner similar to the single intruder case, i.e., multiple single intruders, then matching the density of the surrounding host particles and allowing them to float and swim throughout the sea of host particles could form an ideal mixture.

In order to study this, a series of simulations was run, one where the intruder particles had a higher density than the hosts, one where they had a lower density, and a third where the density of intruder and host were equal. Similar to the single intruder case, the higher- and lower-density intruder particles fell and rose, respectively, as would be expected. The results for a system where the densities are similar are where things get interesting. It was found that the intruder particles would cluster together, forming a raft of particles that would move as a single large entity throughout the sea of host particles. More importantly, it would never break up (during the lifetime of the simulation). The similar density case, which is where an ideal mixture could be formed, displayed the exact opposite result, the system segregated.

The question now becomes, why? Why do these larger intruder particles come together and more importantly, stay together? There is no inherent attraction between them; all the forces in this simulation are repulsive (the disks merely bouncing off one another). So what causes the intruder particles to search each other out in this sea of small hosts? Clearly this is an emergent behavior of the system, one that is not caused by the simple rules governing the dynamics of the program.

By studying a similar system that contains only two intruder particles and keeping track of their distance, they were able to graph the probability that these two intruder particles were a distance 'r' apart. While this may not seem like the most useful data, with it, they were able to calculate an effective attractive force between these intruder particles, even though there is no explicit attraction present in the simulation. It was also noted that this attractive force acted over nearly five diameters of the intruder particles, a range much larger then any of the geometric (bouncing off one another) forces/length scales present in the system. It was also found that in the other cases where the density of the host particles and the intruder particles was not equal that that this force did not exist, or was significantly weakened, to the point of not being able to affect the outcome of the simulation.

With an understanding that there is a collective force causing the intruder particles to segregate themselves from the host particles, the next question one seeks to answer is what is the origin of this force. The research team speculated that this is due to a "ratcheting" effect that the small host particles exert on the larger intruders. During the shaking cycles, the forces acting on the various particles can lead to density variations in the bed [Bottom Figure]. If there is a lower density of host particles between the intruders (Area I) than around them (Areas II and III), then the collisions between host particles and intruders will produce a net force pushing the intruders together (Green arrows in bottom figure). This net force, computed earlier, and described phenomenologically here is what may give rise to this highly non-ideal behavior that is observed.

This research offers up a mechanism that may explain the foundations of why granular mixtures will separate. Since it was also shown that this collective attractive force would be negated when there is a difference in the density of the host and intruder particles, it may provide a basis to search for ways to mitigate this segregation in real-world applications.

Matt Ford / Matt is a contributing writer at Ars Technica, focusing on physics, astronomy, chemistry, mathematics, and engineering. When he's not writing, he works on realtime models of large-scale engineering systems.